Doctor can evaluate. Hand foot mouth disease (hfm) is usually from viruses such as coxsackie virus. Children are the usual patients who get hfm disease, but their parents can also get infected. Parents should see their doctors to verify their illnesses, as other infections (such as strep throat) can cause sore throat and rashes. Coxsackie hfm infections in the U.S. Usually go away on their own without complications.
Not bad. Adults can contract hand-foot-mouth disease following exposure from an infected person. They don't always get the classic rash on their hands, feet, and in the throat as a child usually doses when they get infected. Your sore throat can be from hfm infection. If so, it will get better by itself without any benefit from antibiotics.
Could be... Yes, parents and other adults could catch hand foot and mouth, which is actually a virus, usually caused by coxsackie virus. Most of us have had the infection as a child (just another staple infection for kids) and mostly wont get sick after elementary school age. But, we still could get sick from the virus, its just unusual. It goes away quickly and usually completely benign.